Algebra> What is the remainder when (32^32)^32 is ...

What is the remainder when (32^32)^32 is divided by 7 ?

RO , 8 Years ago

Grade 9

3 Answers

RO

Sorry I know the answer but I myself posted it once again extremely sorry for the disturbance

Regards Poster of this question

Sorry iitans

Last Activity: 8 Years ago

RO

Rem [32^32^32 / 7] = Rem [4^32^32 /7]

Now, we need to observe the pattern
4^1 when divided by 7, leaves a remainder of 4
4^2 when divided by 7, leaves a remainder of 2
4^3 when divided by 7, leaves a remainder of 1

And then the same cycle of 4, 2, and 1 will continue.
If a number is of the format of 4^(3k+1), it will leave a remainder of 4
If a number is of the format of 4^(3k+2), it will leave a remainder of 2
If a number is of the format of 4^(3k), it will leave a remainder of 1

The number given to us is 4^32^32

Let us find out Rem[Power / Cyclicity] t0 find out if it 4^(3k+1) or 4^(3k+2). We can just look at it and say that it is not 4^3k

Rem [32^32/3] = Rem [(-1)^32/3] = 1
=> The number is of the format 4^(3k + 1)
=> Rem [4^32^32 /7] = 4

Last Activity: 8 Years ago